Borda Count to the median

[Mike Rouse]

> Here are some concerns, assuming I understand the method properly.
> Consider the following example:
>
> 45 A B C
> 25 B C A
> 30 C B A
>
> A 45*2+6*0=90
> B 25*2+26*1=76
> C 30*2+21*1=81
>
> So, A wins.  Plurality would also pick A.  Condorcet's method picks
> B.  IRV would pick C.
>
> I see a few problems with A being the winner.
>
> First, A is ranked last by a majority.

You are absolutely correct. I was trying to get around one Borda problem
(being ranked first by a majority and still losing) and left another (being
ranked last by a majority and still winning). Um, my new additional rule is
if there is a majority ranking you last, you can't win! Yeah, that's the
ticket! (Just kidding)

>
> Assuming sincere rankings, if these same voters were asked to pick
> the worst candidate, candidate A would also win for worst candidate
> by the same method.  However, no candidate can be both best and
> worst.
>
> Note that every voter placed B and C together on their ballot (A
> never comes between).  It is therefore possible that B and C
> represent some similar ideology or party.  We can therefore consider
> this an example of vote splitting.

One possibility is to allow multiple votes for first choice (making it even
more like an Approval ballot). The desire to get your first choice into
office would then fight with the desire to strategically vote your biggest
competitor down -- if you give Nader and Gore first place ballots and you
prefer Nader, Gore might win because of it. If you rate Nader above Gore,
Bush might win because of it. I don't see of a way to keep out strategic
voting while still fully counting negative votes (unless it's with the rule
"If a candidate gets a majority of last place votes, he cannot be voted into
office), but a kind of dynamic tension might keep a balance between strategy
and truthfulness. (grin)

> By the way, I recommend you check out my Electoral Methods Resource.
> It isn't an official FAQ, but it tries to fill that kind of role.
>
> http://www.fortunecity.com/meltingpot/harrow/124
>
--
> Blake Cretney
>

Thank you for the response and the link!

Michael Rouse
mrouse at cdsnet.net

PS Has anyone played with fractional valuations of the Borda count? Like
(for instance) all first place votes are 1, all second place votes are 1/2,
all third place are 1/3 (if you are using 1/n) or 1/4 (if you are using
1/2^(n-1)), etc? I'm wondering what strange voting results might occur with
such methods. (I'm thinking of using a golden-mean method where the ratio
between each number remains constant, but that might be too complicated!)

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20001027/5f2565fb/attachment-0003.htm>